White Paper – Image Of Laser From Rayleigh Scattering Directly Correlated To Beam Waist Measurements Of High-Power Lasers

The discovery of Rayleigh Scattering by 3rd Baron Rayleigh, John William Strutt, served an explanation of why the sky is blue during the daytime and different hues of orange, pink, and purple in the early morning hours and at dusk. But it was only recently that this phenomenon has been applied to the measurement of high-powered lasers. Only through the measurement of the laser source and laser system can the user of the laser fully understand its performance and then start to control the processes in which they are used. Key laser parameters which ensure a successful process include output power or energy at the work piece, spot size or beam waist size, spot size location (over time), in addition to M2 or Beam Parameter Product values. Since the beginning of the application of the highpowered laser, and with recent steady increases in continuous-wave power, measurement has proved to be more and more problematic. This paper will discuss how the signal of the laser produced from Rayleigh Scattering can put to rest any concerns by the laser user of damaging their laser measurement equipment. The high-power laser user can now obtain dynamic characteristic measurements, instantly from beam.

Conventional laser beam profiling requires the laser beam to be directly incident upon some type of detection system. In the industry today, typical beam profilers include scanning aperture profilers using slits, knife-edges, or pinholes that utilize single large area detectors, or camera-based profilers using area array detectors such as CCD's or photodiode arrays. The high sensitivity of camera profilers typically requires the laser to be reduced in intensity by many orders of magnitude using beam sampling and optical attenuation. Focused CW lasers in only the 1 Watt range and pulsed lasers in the 1 J range can easily damage scanning apertures, and beams in the kW range can damage beam samplers. The advent of highpower lasers in the kW to 100kW range required a paradigm shift in beam profiling and the Rayleigh scattering of laser light as it propagates through air allows for this shift to be made. New camera-based instruments that measure the Rayleigh scatter provide accurate beam profiles of high power lasers in the kilowatt regime without intercepting the laser beam. Rayleigh scattering is due to the electric polarizability of molecules; specifically oxygen and nitrogen in air for laser beam profiling. The electric field of the laser radiation induces an oscillation of the molecular dipole at the laser frequency, resulting mostly in elastic scattering at the same frequency. The intensity of the Rayleigh scatter is derived from theory of the Hertzian Dipole, and is given by the expression [1]:

Since the scattered light is viewed from the side the scatter angle θ is 90°. The polarizability, α, is problematic for polarized beams but for typical unpolarized fiber lasers and diode lasers it is not of importance. Of primary concern here for laser measurement is the 1/λ4 dependence, (which is why the sky looks blue) which strongly affects the ability to measure the scatter based on the sensitivity of available cameras.

The scattered intensity is on the order of 10-6 of the beam intensity at λ=1070nm, and standard CCD or CMOS cameras with silicon response have sufficient sensitivity for measurement of kW power beams focused to the several mm and less spot size range. However, for CO2 lasers, the scatter is reduced another factor of 104, and there are no detectors that have sufficient sensitivity to measure even a 100kW beam. Thus from a practical perspective only beams in the 1080 range and below can be profiled using CCD or CMOS cameras. The wavelength range can be increased to the ~1800nm range using InGaAs array cameras, but this is at significant cost increase.

Measurement Technique

The scattered laser light is imaged from the side using conventional CCD or CMOS cameras with lenses operating telecentrically. The images are captured digitally and processed to obtain the beam profiles. Both CW and Pulsed lasers can be measured. Since the data is acquired at video rates, the measurements are taken in near real-time, making optical adjustments easier and faster to perform.

A profile is obtained for every column of the detector array, so of major significance here is the ability to capture entire sections of the beam caustic. As an example, for common CCD and CMOS cameras with array sizes of say 1090 × 2048, 2048 profiles are captured simultaneously. Each pixel in a column of the image collects the scattered light from a corresponding chord through the beam, so the resulting profiles are equivalent to those obtained using a scanning slit profiler in the direction of the view.

Instrument Design Considerations

There is a contrasting design requirement that includes both large array size and small pixel size, and lenses that either magnify or de-magnify the beam image. Small pixel size and or lens magnification is needed for small focused beam measurement, in the 50 μm range, and large array size is needed to image focused beam caustics along the path to obtain ~6 Rayleigh ranges for accurate BPP (M2) measurement per the ISO 11146 standard [2].

Thus there are several possible instrument configurations depending on the intended measurement. If only spot size is of importance, then small arrays with small pixel dimension and high magnification can be used. On the other hand, if measurement of M2 and Beam Parameter Product (BPP) is desired, then large arrays and demagnification are required to obtain sufficient Field-of-View.

Instruments can be for single axis measurement, or dual orthogonal axes using two cameras or mirrors to obtain orthogonal profiles using a single camera. It is also possible to obtain multiple views using multiple cameras and mirrors. Also, single axis instrument can be rotated to obtain multiple views at any angle, and tomographic reconstruction can be used to generate more detailed 2D profiles.

ISO 13964 Standard Beam Parameters derived from each profile include [3]:

  • Dslit and D4σ Beam Diameters
  • Beam Focus "Z" Position
  • Beam Centroid Position
  • Beam Power

Measurement of the beam caustic allows determination of M2 parameters from the ISO 11146 least squares hyperbolic fit to the caustic diameters. These parameters are:

  • M2 Beam Propagation Ratio
  • Divergence
  • Waist Position
  • Rayleigh Range
  • Beam Parameter Product (BPP)

The relative Beam Power is also calculated for each profile.

Measurement Examples

Measurements were performed to evaluate the Rayleigh scatter technique and capabilities using various high-power fiber, diode and disk lasers.

Profile Data, ISO Fit, and Beam Parameters

Figure 1 shows a caustic measurement of a disk laser operating at 6kW obtained using a camera with 1392 pixel columns and lens magnification of ~0.4, with equivalent pixel dimension of ~16.125μm. The red points are the raw data for the 1392 profiles, with an observed spread in diameter of approximately10%. The blue curve is the ISO standard curve fit. Since there are so many profiles; 1392 compared to the minimum ISO set of 10, the Law of Averages works in our favor to provide a more accurate beam caustic.

Figure 1. Caustic measurement of a disk laser operating at 6kW. Raw diameters for 1392 profiles are shown in red, the ISO curve fit in blue, and the relative power in green.

The relative power for each profile was also determined and is shown as the green points. This set is seen to be flat as is required by Conservation of Energy in the propagating beam. Table 1 shows all the parameters that can be obtained from the raw profile and the ISO caustic fit.

Table 1. Parameters obtained from the raw profiles and ISO Caustic fit.

Beam Parameter Product

Tables 2 and 3 summarize measurements performed at 2kW and 20kW on different fiber lasers using a scanning pinhole instrument as reference. Considering that the scanning pinhole instrument has accuracy to only approximately the 5% level, the agreement of the Rayleigh results with the reference is excellent.

Table 2. Comparative Measurements of Fiber Laser at 2kW.
Table 3. Comparative Measurements of Fiber Laser at 20kW.

Focus Shift

Measurements of Focus Shift were performed on lasers with transmissive and reflective type delivery heads. Examples of these measurements are shown below in figures 2 and 3.

Figure 2 is for a fiber laser operating at 100kW with reflective delivery head, showing the focal shift in the beam propagation direction "Z". The beam image shown in figure 2a is just after the laser was turned on at t=0s and the image in 2b was at t≅9.8s A shift of ~19mm is observed here. Figure 2c is a time chart of focus position vs frame sample number (81.6ms/frame) recorded for 78.4 seconds at which time the laser was turned off. It shows the shift reducing to ~11mm at this time.

Figure 2. Focal shift measurement in the propagation direction for a fiber laser with reflective delivery head operating at 100kW.

Figure 3 shows time charts for measurement of Focus Shift in the propagation and lateral directions; the"XYZ" shift, for a fiber laser operating at 6kW with transmissive delivery head. (This data for the "Y" shift was obtained by rotating the profiler 90°). Here the shift in the propagation direction is seen to be ~4mm after equilibration at ~16.3s. The corresponding lateral shift is ~100μm in "X" and ~90μm in "Y", for a total lateral shift of ~135μm.

Figure 3. Time charts for measurement of Focus Shift in the propagation and lateral directions, the "XYZ" shift, for a fiber laser with transmissive delivery head operating at 6kW.

Beam Poynting Vector

The centroids of the profiles at the extremes of the caustic can be used to determine the direction of the Poynting Vector in real time. This ability can be used for accurate metrology of beam pointing, and can be used for real-time adjustment of optics.


The Rayleigh Scatter technique has been demonstrated to be an accurate and reliable method for "noncontact" beam profiling of high-power lasers in the nominal 1-100 kW range. When it comes to power, practically the "sky is the limit!" Important laser characteristics such as laser spot (beam waist) size and roundness, beam divergence, and beam caustic measurements such as BPP and M2 can be measured at a near real-time rate. Additionally, the application of this technology also provides important dynamic measurements of laser characteristics such as focus shift in both the propagation and lateral directions, which have never been possible before.

This technique has been incorporated into a commercially available beam profiling system called BeamWatch® made by Ophir-Spiricon. The BeamWatch is being designed for both industrial laser end users and technicians and is intended to be used both as a periodic at-process laser inspection tool and a comprehensive service and troubleshooting tool. The real-time measurements that it provides give a more comprehensive analysis of the laser's performance than historic laser measurement techniques.

Continuing development of this technology is ongoing and could eventually provide more dynamic measurements in the future including Poynting vector measurements which would be useful in beam pointing metrology and real-time laser alignment applications.

Figure 4. Ophir-Spiricon's BeamWatch beam measurement system being used with a 100KW laser beam power measurement system made by Ophir measuring a 100KW fiber laser


  1. http://hyperphysics.phy-astr.gsu.edu/hbase/atmos
  2. International Standard ISO/FDIS 11146-1
  3. International Standard ISO/FDIS 13694
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